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The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-H\"uckel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s₄ₗ can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s₄ₗ-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s₄ₗ-1.
Khrapak et al. (Mon,) studied this question.